Modal and transient analysis of membrane acoustic metasurfaces

Abstract

Dispersive surface waves on an acoustic 2D metamaterial, a metasurface consisting of membranes on a rigid surface, have certain propagation characteristics with potential applications for resonance based sensing and subwavelength imaging. The trapped modes of the system that is responsible for the dispersive properties of these acoustic waves are analyzed through modal analysis for a small linear membrane array to obtain the mode shapes, resonant frequencies, quality factors, and wavenumbers. Transient analysis is used for larger arrays to obtain the dispersive properties of the traveling waves and is compared to the modal analysis. Equifrequency contours of the 2D metasurface illustrate interesting features of the metasurface at different frequency regimes around the membrane resonance. These features include anisotropic wave propagation, directional band gap, negative refraction, and complete band gap. Effects of membrane pitch, randomness of resonance, and aperiodic membrane spacing on dispersion, band gaps, and quality factor of the trapped modes on the metasurface are investigated as they relate to realistic implementations for different applications.